By number of injuries per participant or depth of injury or number of deaths per participant? To define the metric first, then answer the question. Are there a lot of misnomers out there? YES. If you ask John Q Public the question and give him a multiple choice option throwing in "shooting sports" as and option, he/she will most likely rank that pretty high. The truth is shooting sports has an exceptionally safe record with very, very few injuries/deaths per participant compared to almost any other sport. You are much more likely to be injured playing basketball or jogging than participating in hunting, skeet/trap shooting or even paintball. see link. http://www.familiesafield.org/pdf/Injury_page.pdf
Whatever the sport, it seems taking anything to the extreme tends to cause injuries more, or not being prepared for the event, not being rested going into the event, or being distracted in the event are big issues for being injured. Those giving 110% from go are less likely to be injured than when they slack off.